Question

Which function represents a reflection of f(x) = Three-eighths(4)x across the y-axis? g(x) = NegativeThree-eighths (one-fourth) Superscript x g(x) = Negative three-eighths(4)x g(x) = Eight-thirds(4)-x g(x) = Three-eighths(4)–x

Answer 1

The function which represents a reflection of f(x) is

g(x) = Three-eighths $(4)^{-x}$ ⇒ last answer

Step-by-step explanation:

Let us revise the reflection across the axes

• If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
• If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

∵ Three-eighths = $\frac{3}{8}$

∴ $f(x)=\frac{3}{8}(4)^{x}$

∵ f(x) is reflected across the y-axis

- That means the sign of x coordinates of the points on the graph will

  change to opposite

∴ x will change to -x

∴ $g(x)=\frac{3}{8}(4)^{-x}$

The function which represents a reflection of f(x) is

g(x) = Three-eighths $(4)^{-x}$

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Answer 2

Answer:

The function which represents a reflection of f(x) is

g(x) = Three-eighths  ⇒ last answer

Step-by-step explanation:

Let us revise the reflection across the axes

If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)

If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

∵ Three-eighths =

∴

∵ f(x) is reflected across the y-axis

- That means the sign of x coordinates of the points on the graph will

 change to opposite

∴ x will change to -x

∴

The function which represents a reflection of f(x) is

g(x) = Three-eighths